Magistra addit prudentem ducem non solum procedere scire, sed etiam recedere, cum necesse sit.

The main clause is Magistra addit.

• Magistra = the subject, nominative singular, the female teacher
• addit = adds / says in addition

Everything after that gives the content of what she adds.

Because it is the subject of an indirect statement.

After verbs like addit, Latin often uses the accusative + infinitive construction instead of a finite clause with that.

So here:

• prudentem ducem = accusative subject of the reported idea
• scire = infinitive verb of that reported idea

In smoother English, this corresponds to something like that a wise leader knows...

Also notice agreement:

• ducem is accusative singular of dux
• prudentem is accusative singular too, agreeing with ducem

Because the sentence is using indirect statement.

Latin often reports what someone says, thinks, knows, or adds with:

• accusative subject
• infinitive verb

So instead of a direct version like:

• prudens dux ... scit

we get an indirect version after addit:

• prudentem ducem ... scire

That is a very common Latin pattern.

They are complementary infinitives with scire.

Latin often uses scire + infinitive to mean to know how to do something.

So:

• procedere scire = to know how to advance / move forward
• recedere is understood with the same scire
• the full sense is to know not only how to advance, but also how to retreat

Latin does not need to repeat scire after recedere, because it is easily understood from the first half.

This is a very common correlative pair meaning:

• non solum = not only
• sed etiam = but also

Here it balances two infinitives:

• non solum procedere
• sed etiam recedere

So it neatly contrasts two abilities: advancing and retreating.

Because Latin word order is much freer than English word order.

Both ideas are clear from the endings and construction, so Latin can arrange words for emphasis or rhythm. Here, putting procedere before scire helps the sentence flow into the balanced pair:

• non solum procedere scire
• sed etiam recedere

So the order is stylistic, not confusing. The grammar still shows that scire governs the infinitives.

It is a cum-clause meaning something like when it is necessary or whenever it is necessary.

It gives the circumstance under which retreating is appropriate. In sense, it goes especially with recedere:

• a wise leader knows how to retreat when necessary

So it adds an important qualification: retreat is not cowardice here, but good judgment under the right circumstances.

Because cum often takes the subjunctive when it introduces a circumstantial clause.

So:

• cum necesse est would be a more straightforward when it is necessary
• cum necesse sit gives the more classical subordinate sense when/whenever it may be necessary, when circumstances require it

For a learner, the key point is:

• cum + subjunctive is very common in Latin
• here sit is the present subjunctive of esse

Necesse means necessary and is used impersonally.

So necesse est / necesse sit means:

• it is necessary
• it may be necessary

Latin does not need a dummy subject like English it. English says it is necessary, but Latin simply says necessary is.

Also, the thing that is necessary can be left understood from the context. Here the sense is basically:

• when it is necessary [to retreat / to do so]

Because prudens is the nominative form, but here the adjective must agree with ducem in the accusative.

So:

• nominative: prudens dux = a wise leader
• accusative: prudentem ducem = a wise leader as object or as accusative subject in indirect statement

This is a good example of how third-declension adjectives change form to match the noun they describe.

Yes, and that is often the easiest way to understand Latin indirect statement.

A rough direct version would be:

• prudens dux non solum procedere scit, sed etiam recedere, cum necesse est/sit

Then after addit, Latin shifts it into reported form:

• prudentem ducem ... scire

That is a very useful habit for learners: when you see accusative + infinitive, try mentally converting it into a direct statement with a nominative subject and a normal finite verb.